IN TRAINGLE ABC SEG BD BISECT ANGLE ABC IF AB =X BC=X+5 AD=X-2 DC=X+2 THEN FIND THE VALUE OF X
Answers
Step-by-step explanation:
By angle bisector property
x ( x + 2 ) = (x - 2)(x + 5)
2x = 3x - 10
2x - 3x = -10
-x = -10
.°. x = 10
Answer:
The value of x is 10 units.
Step-by-step-explanation:
NOTE: Refer to the attachment for the diagram.
We have given that,
In △ABC,
Seg BD bisects ∠ABC,
AB = x
BC = x + 5
AD = x - 2
DC = x + 2
We have to find the value of x.
Seg BD bisects ∠ABC,
∴ By the property of angle bisector of triangle,
( AB / BC ) = ( AD / DC )
⇒ [ ( x ) / ( x + 5 ) ] = [ ( x - 2 ) / ( x + 2 ) ]
⇒ x ( x + 2 ) = ( x - 2 ) ( x + 5 )
⇒ x² + 2x = x ( x + 5 ) - 2 ( x + 5 )
⇒ x² + 2x = x² + 5x - 2x - 10
⇒ 2x = 3x - 10
⇒ 2x - 3x = - 10
⇒ - x = - 10
⇒ x = 10
The value of x is 10 units.
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Additional Information:
1. Angle bisector theorem:
When a ray bisects an angle, every point on the ray is equidistant from the both arms of the angle.
2. Angle bisector theorem of triangle:
When a ray bisects an angle of a triangle, the arms of the angle and the remaining two sides are in the proportion.
3. This theorem is based on Basic Proportionality Theorem ( BPT ).